Sound rendering or auditory displays can augment graphical rendering and provide the user with an enhanced spatial sense of presence. Sound propagation in a scene refers to the modeling of the sound heard by the listener after the sound emitted from each source undergoes reflections, diffraction and absorption through the scene. Some of the driving applications of sound rendering include acoustic design of architectural models or outdoor scenes, walkthroughs of large CAD models with sounds of machine parts or moving people, urban scenes with traffic, and computer games, among others. The computation of sound propagation paths can take into account the knowledge of sound sources, listener locations, the 3D model of the environment, and material absorption and scattering properties.
Preferably, the modeling of sound propagation effects can further account for different wave propagation phenomena such as specular reflections, scattering (including diffuse reflections and edge diffraction), interference, and other phenomena. In particular, with respect to modeling of diffuse reflections, for instance, which are considered important for modeling sound propagation, many objective and perceptual studies have been conducted to ascertain the importance of diffuse reflections for sound propagation. Further, it is computationally challenging to model high orders of diffuse reflection. Thus, due to its importance and computational challenge, modeling diffuse reflections for sound propagation is an active area of interest in many sound rendering applications.
At a broad level, sound propagation algorithms can be classified into numerical and geometric methods. Numerical methods attempt to directly compute numerical solutions to the acoustic wave equation. The propagation of sound in a medium is governed by the acoustic wave equation, a second-order partial differential equation. Several techniques (e.g., finite difference time-domain method) are known for directly solving the wave equation using numerical methods and accurately modeling sound propagation in a scene. Modeling diffuse reflections is essentially a matter of specifying appropriate boundary conditions to the numerical solver and performing the simulation on a grid fine enough to capture the detailed “roughness” of the surfaces that results in acoustic wave scattering. However, despite recent advances, these methods can be rather slow and are mainly limited to simple static sources, at least the in part because the complexity of these methods is proportional to the volume of the scene and the fourth power of the maximum frequency of sound simulated, and thus can be very slow for large acoustic spaces or high frequency sound sources.
To address these issues, precomputation-based methods have been developed that use a numerical simulator to compute the acoustic response of a scene from several sampled source positions such that, at runtime, these responses are interpolated given the actual source position. These methods are faster, but require large amounts of precomputed data.
In terms of geometric sound propagation, two standard methods used to simulate diffuse sound reflections are based on ray (or volume) tracing and radiance transfer. Most sound propagation techniques used in practical applications model the acoustic effects of an environment in terms of linearly propagating rays or 3D volumes. These geometric acoustics techniques are not as accurate as numerical methods in terms of solving the wave equation, and cannot easily model all kinds of propagation effects, but allow efficient simulation of early reflections. For instance, methods based on ray tracing are able to model both diffuse and specular reflections of sound. Since early specular reflections provide the listener with important perceptual cues regarding the direction of sound, specialized techniques have been developed for modeling specular reflections, which include volume tracing and the image source method. For static scenes, which frequently arise in architectural acoustics and virtual environments, radiance transfer methods can be used to simulate reflections from surfaces with arbitrary bidirectional reflectance distribution functions (BRDFs). Many techniques have also been designed to simulate edge diffraction.
Accordingly, conventional numerical and geometric methods each have significant disadvantages that limit their abilities to effectively simulate diffuse reflections (or specular reflections, edge diffraction, etc.) of sound in real time.